Think about all of the things you do outside of work or school. Lots of people have hobbies and activities that they like to participate in during their free time. Others have interests that they like to pursue. Many people have some sort of sport or game as a hobby or interest that they enjoy. Sports and games can be fun, physical, and good for your brain! Have you ever stopped to think about just how much math is involved with sports and games? It may be more than you think!
The most obvious example of math in sports is, of course, the scoring. Every sport has its own system, most of which take a bit of arithmetic to keep track of. Some sports, like baseball, use a simple scoring system where each time a team scores, they get one point. Some sports use a slightly different, more varied system. For example, in American football, each touchdown earns six points; a bonus field goal will add one more. A field goal not following a touchdown earns three points, and the variety doesn't stop there.
There are many uses for math in sports that don't relate to scoring. The skills of professional athletes can be compared by looking at their stats, which vary with the sport the athlete plays. You could look at how often a baseball player hits the ball, or how many times a defensive player on a football team has sacked the opposing team's quarterback. These stats make it easy for fans to understand the inner workings of each team and for coaches to decide who to put on the team with each new season.
For many more ways that mathematics can be utilized in sports and for interesting information and application exercises, visit this website.
Monday, April 30, 2012
Wednesday, April 25, 2012
Oh, the places you'll go...with math!
The school year is almost over! What will you be doing with your summer break? Lots of people choose to go on trips or vacations during the summer. Did you ever stop to realize how much math is involved with going on vacation? It's everywhere! From the money you'll spend to how far you'll travel to any plans you'll have once you get there, you'll be using a lot of math to plan your trip!
Imagine that you live in Birmingham, AL and you'll be traveling to Atlanta, GA this summer. There are a lot of things to take into account. More than likely, you'll be driving there. The distance is so short that it isn't worth the money to take a plane. The distance between Birmingham and Atlanta is roughly 160 miles. If the average speed limit between these two locations is 60 mph, how long will it take you to get there? Some simple arithmetic (160/60) tells us that it will take about 2 hours and 45 minutes to get there.
If you leave your house at 1 pm on the day of your trip, what time will it be when you arrive in Atlanta? Here, we have to take a little bit of extra information into account. Birmingham is located in the Central Time Zone of the United States, while Atlanta is located in the Eastern Time Zone. The difference between these locations is one hour. So if you leave at 1 pm Birmingham time, you'll actually be leaving at 2 pm Atlanta time. Take into account the 2 hours and 45 minutes you have to drive, and you'll arrive in Atlanta at around 4:45 pm. When coming back to Birmingham, you have to get rid of that extra hour when figuring out times. So if you leave at 1 pm Atlanta time to come back, you're actually leaving at noon Birmingham time. You'll arrive in Birmingham at around 2:45 pm.
How much gas will you have to buy? Suppose your car gets 25 miles to the gallon. If you're traveling the 160 miles it takes to get to Atlanta, then your car will use about 6 and a half gallons of gas to get there. Suppose gas is $3.00 a gallon. What is the minimum amount you'll have to pay for gas? Take 6.5 times $3.00 and you'll get about $19.50, which is the least amount you have to spend on gas to get there.
Leaving tomorrow and need to figure out all your numbers quickly? This site is a very handy tool which does just that. Input your times, budget, and other figures and you'll get all the information you need. Of course, if you're not leaving tomorrow, take some time to figure out what you'll need! It's good exercise for your brain, and it's fun!
Wednesday, April 18, 2012
The Sweet Sound of Subdivisions
If you're like most people, the first thing you do after getting into the car to go somewhere is turn on the radio. Music is a very popular part of many cultures, and it is often regarded as a universal language. Believe it or not, mathematics is the foundation of music as we know it. Almost all the aspects of music, from notes and chords to rhythms and tempos, are based on numerical values that fit well together.
The rhythm of a piece of music is based on fractions and is determined by a notation called a time signature. The time signature tells the musician how many beats are in a measure of music and which note to count as the beat. For example, the common time signature, 4/4, signifies four beats in a single measure and the quarter note getting the beat. The time signature 3/8 signifies three beats in a measure with the eighth note getting the beat. Subdivision, or splitting the beats into parts, is based largely on fractions as well. The names of the notes are indicative of this. The longest note in music is called a whole note. A note that is half as long as a whole note is called a half note. Half of a whole note is a quarter note, and so on with eighth notes, sixteenth notes, thirty-second notes, and sixty-fourth notes.
The notes and chords that make up the melodies and harmonies of a song are chosen based on a number of factors, but the reason they sound good together is thanks to sound waves and their frequencies. The frequencies of different notes create the sound we hear, called a pitch. Pitches that are certain distances apart produce a certain type of sound, and this is what creates intervals, or the sound produced by combinations of notes played at the same time. You may have heard of an arpeggio, which is comprised of the first, third, and fifth notes of a scale. These intervals are called thirds and are very pleasing to the ear. If the notes are too close, however, they may clash. This creates a sound that is harsh and unpleasant, and is therefore rarely used in the music and you and I listen to.
The rhythm of a piece of music is based on fractions and is determined by a notation called a time signature. The time signature tells the musician how many beats are in a measure of music and which note to count as the beat. For example, the common time signature, 4/4, signifies four beats in a single measure and the quarter note getting the beat. The time signature 3/8 signifies three beats in a measure with the eighth note getting the beat. Subdivision, or splitting the beats into parts, is based largely on fractions as well. The names of the notes are indicative of this. The longest note in music is called a whole note. A note that is half as long as a whole note is called a half note. Half of a whole note is a quarter note, and so on with eighth notes, sixteenth notes, thirty-second notes, and sixty-fourth notes.
The notes and chords that make up the melodies and harmonies of a song are chosen based on a number of factors, but the reason they sound good together is thanks to sound waves and their frequencies. The frequencies of different notes create the sound we hear, called a pitch. Pitches that are certain distances apart produce a certain type of sound, and this is what creates intervals, or the sound produced by combinations of notes played at the same time. You may have heard of an arpeggio, which is comprised of the first, third, and fifth notes of a scale. These intervals are called thirds and are very pleasing to the ear. If the notes are too close, however, they may clash. This creates a sound that is harsh and unpleasant, and is therefore rarely used in the music and you and I listen to.
Wednesday, April 11, 2012
Some Delicious Links for You!
If you're reading this blog right now, you're using a type of technology called Web 2.0. Web 2.0 is defined as the various internet technologies that allow average users to create and publish material online without having to rely on a specialized knowledge of coding. These technologies include blogs, wikis, social networking sites such as Facebook, sharing websites such as YouTube and Flickr, and online forums. These technologies are now working their way into classrooms around the world to enhance the world of education.
Using Web 2.0 internet technology is sure to change the face of education drastically and for the better. As this new way of teaching and learning emerges, so too do sources of information and new ideas on the subject. I've compiled a list of links related to this subject on a social bookmarking site called Delicious. These links range from news stories to reference sites to YouTube videos. Check them out, see what you think! The information they have to offer is through and diverse. Chances are you'll learn something new! To view my Delicious page, click here.
Wednesday, April 4, 2012
Money...It's what I want!
In this day and age, money seems to be the thing that makes the world go 'round. Money can get you food, transportation, entertainment, and higher education, among other things. You've probably already heard plenty about how mathematics can be used when earning or spending money. But what about the process of saving money? How can math be used on money that isn't going anywhere?
The answer lies in budgeting and investing. A budget is a plan that people use to limit the amount of money they can spend on various things. For example, you might limit yourself to spending only $30 per month on eating out, or you may use sales and coupons to ensure that your monthly grocery bill doesn't go above $300. Budgets can also be drawn up in the form of percentages. Suppose that 60% of your monthly income goes toward necessary expenses, such as a power bill or a car payment. Then you have 40% of your income left to budget toward expenses with flexible costs.
A good way to save money (and to gain a little extra in the process!) is by putting some in a savings account. Savings accounts are typically associated with an interest rate, or a percentage of the total money that gets added back in over regular intervals. Some savings accounts have interest that is compounded biweekly or monthly, while others are compounded continuously. Mathematics can help you calculate the amount of money that you can earn by keeping your money in a savings account. For example, if you invest $100 in a savings account that earns 5% interest compounded monthly, then your account will have $105 in it one month after your initial deposit.
Be smart with mathematics to be smart about money! For more information about savings accounts and compounded interest, click here.
The answer lies in budgeting and investing. A budget is a plan that people use to limit the amount of money they can spend on various things. For example, you might limit yourself to spending only $30 per month on eating out, or you may use sales and coupons to ensure that your monthly grocery bill doesn't go above $300. Budgets can also be drawn up in the form of percentages. Suppose that 60% of your monthly income goes toward necessary expenses, such as a power bill or a car payment. Then you have 40% of your income left to budget toward expenses with flexible costs.
A good way to save money (and to gain a little extra in the process!) is by putting some in a savings account. Savings accounts are typically associated with an interest rate, or a percentage of the total money that gets added back in over regular intervals. Some savings accounts have interest that is compounded biweekly or monthly, while others are compounded continuously. Mathematics can help you calculate the amount of money that you can earn by keeping your money in a savings account. For example, if you invest $100 in a savings account that earns 5% interest compounded monthly, then your account will have $105 in it one month after your initial deposit.
Be smart with mathematics to be smart about money! For more information about savings accounts and compounded interest, click here.
Wednesday, March 28, 2012
Adding a few homey touches...with mathematics!
Imagine you've just taken a big step and bought the house of your dreams! It's very big and contains all the bells and whistles...but it doesn't scream "YOU!" just yet. Decorating is an important step in the process of making a house into a home. You'll need to pick out colors, patterns, accessories, and more...and don't forget the math!
Oh yes, mathematics is essential to home decoration! Don't believe me? Suppose you're trying to pick out a new sofa to put in your living room. You want one that's nice and big so that all of your friends and family can sit on it and visit with each other. But how big is too big? How will you know how much space this sofa will take up? What if it doesn't fit? Grab your tape measure and start calculating some areas! Find the area of the space you'd like to put the sofa in, and decide how much space you'd like for it to take up. Then take those dimensions with you when you shop so that you know what you're looking for!
What if you'd like to put in some fancy plush carpet? Putting new carpeting or flooring in a house can get expensive. The last thing you want to do is order too much or go over your budget. Back to finding areas! You'll need to take every nook and cranny of the room into account. The best way to do this is to split the room into many rectangles or other simple polygons. If you can find the areas of the smaller pieces, then you can add them together to get the area of the whole room. Some simple multiplication can help you compare prices and decide which carpet suits your budget best.
There are many other ways that math is useful in home decorating. For examples of the ideas I've shared and for additional ideas, see this page.
Oh yes, mathematics is essential to home decoration! Don't believe me? Suppose you're trying to pick out a new sofa to put in your living room. You want one that's nice and big so that all of your friends and family can sit on it and visit with each other. But how big is too big? How will you know how much space this sofa will take up? What if it doesn't fit? Grab your tape measure and start calculating some areas! Find the area of the space you'd like to put the sofa in, and decide how much space you'd like for it to take up. Then take those dimensions with you when you shop so that you know what you're looking for!
What if you'd like to put in some fancy plush carpet? Putting new carpeting or flooring in a house can get expensive. The last thing you want to do is order too much or go over your budget. Back to finding areas! You'll need to take every nook and cranny of the room into account. The best way to do this is to split the room into many rectangles or other simple polygons. If you can find the areas of the smaller pieces, then you can add them together to get the area of the whole room. Some simple multiplication can help you compare prices and decide which carpet suits your budget best.
There are many other ways that math is useful in home decorating. For examples of the ideas I've shared and for additional ideas, see this page.
Wednesday, March 14, 2012
Countable Cooking
Have you ever cooked an entire meal on your own? Maybe you've baked some cookies or a cake. Perhaps you've prepared something simple such as an ice cream sundae or a pitcher of lemonade. Chances are that you were doing mathematics without even realizing it! The mathematics of cooking goes far beyond counting the quantities of ingredients that you need to add.
Suppose that you begin a recipe only to realize that you don't have enough flour to add what the recipe calls for. You decide that you'll continue with the recipe and end up with a smaller amount of final product. But wait! If the amount of flour is smaller, the amounts of all the other ingredients have to be smaller too, otherwise you risk turning your yummy treats into inedible garbage. In this instance, you can use ratios to look at the proportions of ingredients to each other. For instance, if you originally needed 2 cups of flour and 4 eggs but you only have 1 cup of flour, then you will only need 2 eggs. 2/4 = 1/2.
What if you have an amazing recipe you want to try for a party, but the yield is not as large as you need it to be? Maybe the recipe yields 5 servings, but you need for there to be 20 servings. Since 5 x 4 = 20, you need to multiply all of your ingredient quantities by 4. This is another example of using proportions in cooking.
This link provides further explanation as well as more examples if you'd like to learn more.
Suppose that you begin a recipe only to realize that you don't have enough flour to add what the recipe calls for. You decide that you'll continue with the recipe and end up with a smaller amount of final product. But wait! If the amount of flour is smaller, the amounts of all the other ingredients have to be smaller too, otherwise you risk turning your yummy treats into inedible garbage. In this instance, you can use ratios to look at the proportions of ingredients to each other. For instance, if you originally needed 2 cups of flour and 4 eggs but you only have 1 cup of flour, then you will only need 2 eggs. 2/4 = 1/2.
What if you have an amazing recipe you want to try for a party, but the yield is not as large as you need it to be? Maybe the recipe yields 5 servings, but you need for there to be 20 servings. Since 5 x 4 = 20, you need to multiply all of your ingredient quantities by 4. This is another example of using proportions in cooking.
This link provides further explanation as well as more examples if you'd like to learn more.
Wednesday, March 7, 2012
A few resources for those who are interested!
So...you're big on education, you're big on mathematics. Then you think about combining the two and you automatically think of lecture! Note-taking! Definitions! Theorems! And once graduation comes around, out the window it goes. After all, you can use a calculator all you want now!
While this may be the case for some people, others use more math in their daily lives than most people realize. Think about architects. Imagine if they didn't use math when sketching blueprints. We'd certainly have a lot of crooked buildings. Imagine if chefs never used math in the kitchen. Things would probably taste a little funky. And if doctors didn't use math, you may not be alive to be reading this blog right now.
For anyone who's curious or wants to learn more about the quest to bring reality back to the math classroom, I've compiled a list of great Twitter feeds that are relevant to the topic. You can find it here: https://twitter.com/#!/emmihelin/math-in-real-life
For your place of residence, your health care, and for the perfectly rectangular screen you're reading this on right now, be sure to thank a mathematician! :)
While this may be the case for some people, others use more math in their daily lives than most people realize. Think about architects. Imagine if they didn't use math when sketching blueprints. We'd certainly have a lot of crooked buildings. Imagine if chefs never used math in the kitchen. Things would probably taste a little funky. And if doctors didn't use math, you may not be alive to be reading this blog right now.
For anyone who's curious or wants to learn more about the quest to bring reality back to the math classroom, I've compiled a list of great Twitter feeds that are relevant to the topic. You can find it here: https://twitter.com/#!/emmihelin/math-in-real-life
For your place of residence, your health care, and for the perfectly rectangular screen you're reading this on right now, be sure to thank a mathematician! :)
Wednesday, February 29, 2012
AND NOW FOR SOMETHING COMPLETELY DIFFERENT, PART 3!!
Well, for some reason after publishing this post the first time, none of the text went with it. There's a nice title there for you to look at, but no post. Let's see if it will work this time...
So, contrary to the normal voice of this blog (taking things from inside the classroom and bringing them outside), today we're talking about bringing the technology you use outside of school every day to the classroom. iPhones, MP3 players, tablet PCs and more are all coming to a school near you!
The reasoning has nothing to do with the prevalence and popularity of Angry Birds or Doodle Jump. There are plenty of educational apps and tools available on these platforms, many of which are free. And why not bring these technologies to the classroom? Most students use these same technologies outside of school on a daily basis, so if they're comfortable with them, why not use them in the learning process as well? The current generation of students has grown up around technology and will be around it for the rest of their lives. Soon, almost all schools will have a technologically integrated curriculum. The times are a'changing faster than you can say "Facebook." The question is, can you keep up?
So, contrary to the normal voice of this blog (taking things from inside the classroom and bringing them outside), today we're talking about bringing the technology you use outside of school every day to the classroom. iPhones, MP3 players, tablet PCs and more are all coming to a school near you!
The reasoning has nothing to do with the prevalence and popularity of Angry Birds or Doodle Jump. There are plenty of educational apps and tools available on these platforms, many of which are free. And why not bring these technologies to the classroom? Most students use these same technologies outside of school on a daily basis, so if they're comfortable with them, why not use them in the learning process as well? The current generation of students has grown up around technology and will be around it for the rest of their lives. Soon, almost all schools will have a technologically integrated curriculum. The times are a'changing faster than you can say "Facebook." The question is, can you keep up?
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